Timeline for Étale homotopy type of $\text{Spec}(\mathbb{Z}) \cup \{ \text{place}_\infty \}$
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Sep 27, 2020 at 12:19 | comment | added | user164442 | how many connected components does your thing have? | |
| Sep 25, 2020 at 12:09 | history | edited | user30211 | CC BY-SA 4.0 |
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| Sep 25, 2020 at 7:29 | comment | added | Piotr Achinger | I'm okay with a broad scope, I was more concerned with the set of possible precise formulations of your question being empty. | |
| Sep 25, 2020 at 5:08 | comment | added | Denis Nardin | @DeanYoung Can you give a pointer to where the pro-smooth topos of $\mathrm{Spec}\,\mathbb{Z}\cup\{\infty\}$ is defined? I have no idea of what you're referring to. Note that $\mathrm{Spec}\,\mathbb{Z}\cup\{\infty\}$ is not a scheme, so the general definitions do not apply. | |
| Sep 24, 2020 at 22:53 | comment | added | user30211 | I like to think in terms of the pro-smooth topos (filtered limits of smooth maps). This might not have a candidate for a weakly contractible cover, though (I haven’t found one). Certainly the ordinary smooth topos does not. I respect your concern for a grounded question. But it seems from what @DenisNardin is saying that in choosing the topos, I might only get one or a few of the proposals and a limited perspective. I would much rather hear a broad answer overviewing the current state of the literature than limit myself to a partial view by committing myself to a particular topos. | |
| Sep 24, 2020 at 13:15 | comment | added | Piotr Achinger | This question has already 5 upvotes but still doesn't make sense. Please clarify what you mean by $\operatorname{Spec} \mathbf{Z} \cup \{{\rm place}_\infty\}$ or its etale homotopy type. | |
| Sep 24, 2020 at 2:05 | history | edited | user30211 | CC BY-SA 4.0 |
edited title
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| Sep 23, 2020 at 6:14 | comment | added | Denis Nardin | What topos corresponds to $\operatorname{Spec}(\mathbb{Z})\cup\{\infty\}$? I know of a couple of proposals, but they're both in a rather embrional stage... | |
| Sep 23, 2020 at 5:34 | comment | added | naf | What is your definition of etale homotopy type after adding the infinite place? | |
| Sep 23, 2020 at 3:18 | comment | added | David Roberts♦ | no probs, that would make it a different question :-) | |
| Sep 23, 2020 at 0:52 | history | edited | user30211 | CC BY-SA 4.0 |
added 203 characters in body
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| Sep 23, 2020 at 0:50 | comment | added | user30211 | @DavidRoberts I intended to compactify it first; I hope you don't mind if I change it to $\text{Spec}(\mathbb{Z}) \cup \{ \text{place}_{\infty} \}$. | |
| Sep 23, 2020 at 0:06 | review | Close votes | |||
| Sep 23, 2020 at 20:13 | |||||
| Sep 22, 2020 at 23:48 | comment | added | David Roberts♦ | Does this answer your question? What are the higher homotopy groups of Spec Z ? | |
| Sep 22, 2020 at 23:44 | comment | added | David Roberts♦ | shall we close this as duplicate? | |
| Sep 22, 2020 at 21:01 | comment | added | user30211 | Shoot, I intended to compactify. | |
| Sep 22, 2020 at 20:56 | comment | added | David Roberts♦ | Ok,. Try this: mathoverflow.net/a/186140/4177 | |
| Sep 22, 2020 at 20:53 | comment | added | David Roberts♦ | And $\pi_1=0$ ? | |
| Sep 22, 2020 at 19:47 | history | asked | user30211 | CC BY-SA 4.0 |